34/21: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 34/21
| Monzo = 1 -1 0 -1 0 0 1
| Cents = 834.17450
| Name = septendecimal supraminor sixth
| Name = septendecimal supraminor sixth
| Color name = 17or6, soru 6th
| Color name = 17or6, soru 6th
| FJS name = m6<sup>17</sup><sub>7</sub>
| Sound = ji-34-21-csound-foscil-220hz.mp3
| Sound = ji-34-21-csound-foscil-220hz.mp3
}}
}}
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'''34/21''' is the '''septendecimal supraminor sixth'''.
'''34/21''' is the '''septendecimal supraminor sixth'''.


This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 34/21 is ~1.1 [[cent|¢]] sharp of the golden ratio.
This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 34/21 is ~1.1 [[cent|¢]] sharp of the golden ratio. Two fall short of [[21/8]] and three of them fall short of [[17/4]] by [[9261/9248]], which becomes particularly significant in [[Sephiroth]] temperament.


== See also ==
== See also ==
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* [[Gallery of just intervals]]
* [[Gallery of just intervals]]


[[Category:17-limit]]
[[Category:Sixth]]
[[Category:Sixth]]
[[Category:Supraminor sixth]]
[[Category:Supraminor sixth]]
[[Category:Golden ratio approximations]]
[[Category:Golden ratio approximations]]
[[Category:Pages with internal sound examples]]
{{todo|expand}}
{{todo|expand}}

Latest revision as of 12:10, 24 October 2024

Interval information
Ratio 34/21
Factorization 2 × 3-1 × 7-1 × 17
Monzo [1 -1 0 -1 0 0 1
Size in cents 834.1745¢
Name septendecimal supraminor sixth
Color name 17or6, soru 6th
FJS name [math]\displaystyle{ \text{m6}^{17}_{7} }[/math]
Special properties reduced
Tenney height (log2 nd) 9.47978
Weil height (log2 max(n, d)) 10.1749
Wilson height (sopfr(nd)) 29

[sound info]
Open this interval in xen-calc

34/21 is the septendecimal supraminor sixth.

This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the golden ratio. In this case, 34/21 is ~1.1 ¢ sharp of the golden ratio. Two fall short of 21/8 and three of them fall short of 17/4 by 9261/9248, which becomes particularly significant in Sephiroth temperament.

See also